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Enhanced gauge groups in N=4 topological amplitudes and Lorentzian Borcherds algebras

S. Hohenegger ; Daniel Persson (Institutionen för fundamental fysik, Matematisk fysik)
Physical Review D (1550-7998). Vol. 84 (2011), 10,
[Artikel, refereegranskad vetenskaplig]

We continue our study of algebraic properties of N = 4 topological amplitudes in heterotic string theory compactified on T(2), initiated in arXiv:1102.1821. In this work we evaluate a particular one-loop amplitude for any enhanced gauge group h subset of e(8) circle plus e(8), i.e. for arbitrary choice of Wilson line moduli. We show that a certain analytic part of the result has an infinite product representation, where the product is taken over the positive roots of a Lorentzian Kac-Moody algebra g(++). The latter is obtained through double extension of the complement g = (e(8) circle plus e(8))/h. The infinite product is automorphic with respect to a finite index subgroup of the full T-duality group SO(2, 18; Z) and, through the philosophy of Borcherds-Gritsenko-Nikulin, this defines the denominator formula of a generalized Kac-Moody algebra G(g(++)), which is an 'automorphic correction' of g(++). We explicitly give the root multiplicities of G(g(++)) for a number of examples.

Nyckelord: theta-function identities, automorphic-forms, bps states, couplings, strings, constants, lattices, curves, series



Denna post skapades 2011-12-09.
CPL Pubid: 149868

 

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Institutioner (Chalmers)

Institutionen för fundamental fysik, Matematisk fysik (2005-2013)

Ämnesområden

Astronomi, astrofysik och kosmologi
Matematisk fysik

Chalmers infrastruktur